Highest Common Factor of 42, 74, 21 using Euclid's algorithm
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 42, 74, 21 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 42, 74, 21 is 1 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.
Consider we have numbers 42, 74, 21 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b
Highest common factor (HCF) of 42, 74, 21 is 1.
HCF(42, 74, 21) = 1
HCF of 42, 74, 21 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 42, 74, 21 is 1.
Highest Common Factor of 42,74,21 is 1
Step 1: Since 74 > 42, we apply the division lemma to 74 and 42, to get
74 = 42 x 1 + 32
Step 2: Since the reminder 42 ≠ 0, we apply division lemma to 32 and 42, to get
42 = 32 x 1 + 10
Step 3: We consider the new divisor 32 and the new remainder 10, and apply the division lemma to get
32 = 10 x 3 + 2
We consider the new divisor 10 and the new remainder 2, and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 42 and 74 is 2
Notice that 2 = HCF(10,2) = HCF(32,10) = HCF(42,32) = HCF(74,42) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 21 > 2, we apply the division lemma to 21 and 2, to get
21 = 2 x 10 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 21 is 1
Notice that 1 = HCF(2,1) = HCF(21,2) .
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Frequently Asked Questions on HCF of 42, 74, 21 using Euclid's Algorithm
1. What is the Euclid division algorithm?
Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.
2. what is the HCF of 42, 74, 21?
Answer: HCF of 42, 74, 21 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 42, 74, 21 using Euclid's Algorithm?
Answer: For arbitrary numbers 42, 74, 21 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.